Router-Expert Alignment Analysis

This report performs SVD-based alignment analysis between router vectors and expert weight matrices.

Plot Explanations

The following section explains what each plot type shows and how it is computed. All plots use layer numbers (e.g., L5, L10) in their legends, without timestamps.

Comparison Plots

Comparison Plots: This figure contains four subplots comparing multiple analysis runs:

Cos²(θ) Expert Comparison

Cos²(θ) Expert Comparison: This figure compares cos²(θ) values across experts and layers (for k=1 only):

Shuffle Statistics

Shuffle Statistics: This figure shows statistics from shuffled baseline comparisons:

Z-score Decomposition

Z-score Decomposition: This figure breaks down the z-score calculation into its components:

Distribution Comparison

Distribution Comparison: This plot shows the probability distribution of shuffled alignments (projection energies) compared to the true alignment value:

Per-Expert Breakdown

Per-Expert Breakdown: This figure provides detailed expert-level analysis:

Complete Analysis Visualization

Complete Analysis Visualization: This comprehensive figure contains 12 subplots showing all key metrics for a single analysis run: All metrics are computed as described in the individual plot explanations above.

1. Comparison Across All Runs

This section compares all 6 result files side by side.

Comparison Plots

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Comparison Plots

Cos²(θ) Expert Comparison

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Cos²(θ) Expert Comparison

Diagnostic Plots (Comparison)

Diagnostic plots comparing all runs to understand differences in alignment, z-score, and delta.

Shuffle Statistics

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Shuffle Statistics

Z-score Decomposition

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Z-score Decomposition

Distribution Comparison (k=32)

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Distribution Comparison (k=32)

Distribution Comparison (k=128)

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Distribution Comparison (k=128)

Distribution Comparison (k=512)

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Distribution Comparison (k=512)

Distribution Comparison (k=2048)

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Distribution Comparison (k=2048)

Per-Expert Breakdown

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Per-Expert Breakdown

2. Individual Analysis - Run 1

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.095886 0.083623 2.767175 0.095642 0.095886
2 0.096110 0.081791 2.544904 0.095622 0.000000
4 0.096928 0.083131 2.722896 0.095951 0.000000
8 0.105326 0.085136 2.479962 0.103373 0.000000
16 0.122886 0.091767 2.635744 0.118980 0.000000
32 0.145117 0.090595 2.689427 0.137305 0.000000
64 0.173137 0.080351 2.325970 0.157512 0.000000
128 0.228232 0.083211 2.313799 0.196982 0.000000
256 0.308274 0.092401 2.296443 0.245774 0.000000
512 0.429478 0.095819 1.903831 0.304478 0.000000
1024 0.594914 0.085419 1.779300 0.344914 0.000000
2048 0.782698 0.052253 1.832639 0.282698 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.095886

Max cos²(θ): 0.113289

Min cos²(θ): 0.081037

Std cos²(θ): 0.011979

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.087693 0.087692
1 0.088284 0.088284
2 0.101300 0.101300
3 0.111540 0.111540
4 0.097033 0.097033
5 0.113289 0.113289
6 0.081037 0.081037
7 0.086911 0.086911

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

3. Individual Analysis - Run 2

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.072366 0.063612 2.790334 0.072121 0.072366
2 0.072696 0.062340 2.555272 0.072208 0.000000
4 0.074890 0.064735 2.673774 0.073913 0.000000
8 0.076754 0.064113 2.463954 0.074800 0.000000
16 0.082027 0.068644 2.692019 0.078121 0.000000
32 0.100164 0.082604 2.779862 0.092352 0.000000
64 0.117190 0.091304 2.653731 0.101565 0.000000
128 0.158847 0.116712 2.598195 0.127597 0.000000
256 0.215059 0.145011 2.727091 0.152559 0.000000
512 0.307792 0.183919 2.608082 0.182792 0.000000
1024 0.464653 0.234680 2.436636 0.214653 0.000000
2048 0.682809 0.239296 2.770397 0.182809 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.072366

Max cos²(θ): 0.082854

Min cos²(θ): 0.059842

Std cos²(θ): 0.009443

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.076257 0.076257
1 0.080060 0.080060
2 0.059842 0.059842
3 0.082841 0.082841
4 0.063383 0.063383
5 0.062867 0.062867
6 0.082854 0.082854
7 0.070820 0.070820

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

4. Individual Analysis - Run 3

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.071958 0.060979 2.712114 0.071714 0.071958
2 0.083511 0.068067 2.440966 0.083023 0.000000
4 0.103484 0.083800 2.616887 0.102507 0.000000
8 0.118817 0.088900 2.314535 0.116864 0.000000
16 0.149789 0.108853 2.532124 0.145882 0.000000
32 0.183115 0.126321 2.636953 0.175302 0.000000
64 0.227703 0.143941 2.468127 0.212078 0.000000
128 0.287316 0.169768 2.421234 0.256066 0.000000
256 0.361914 0.201321 2.540398 0.299414 0.000000
512 0.448173 0.220829 2.405310 0.323173 0.000000
1024 0.556532 0.223693 2.230740 0.306532 0.000000
2048 0.720768 0.205407 2.433975 0.220768 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.071958

Max cos²(θ): 0.106940

Min cos²(θ): 0.056461

Std cos²(θ): 0.016288

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.106940 0.106940
1 0.078474 0.078474
2 0.064948 0.064948
3 0.074671 0.074671
4 0.056461 0.056461
5 0.074265 0.074265
6 0.060473 0.060473
7 0.059433 0.059433

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

5. Individual Analysis - Run 4

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.073495 0.061777 2.535697 0.073251 0.073495
2 0.085189 0.068171 2.394850 0.084701 0.000000
4 0.098532 0.075852 2.536124 0.097556 0.000000
8 0.115838 0.083475 2.319364 0.113885 0.000000
16 0.145283 0.100287 2.448533 0.141377 0.000000
32 0.180897 0.119697 2.637595 0.173085 0.000000
64 0.217590 0.130625 2.390451 0.201965 0.000000
128 0.263065 0.145904 2.430203 0.231815 0.000000
256 0.325066 0.167764 2.510164 0.262566 0.000000
512 0.399251 0.177589 2.334718 0.274251 0.000000
1024 0.505917 0.180667 2.177440 0.255917 0.000000
2048 0.672919 0.161160 2.253222 0.172919 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.073495

Max cos²(θ): 0.111711

Min cos²(θ): 0.051174

Std cos²(θ): 0.019774

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.068715 0.068715
1 0.055104 0.055104
2 0.072262 0.072262
3 0.051174 0.051174
4 0.111711 0.111711
5 0.086037 0.086037
6 0.060293 0.060293
7 0.082666 0.082666

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

6. Individual Analysis - Run 5

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.057551 0.047232 2.554473 0.057307 0.057551
2 0.059381 0.047484 2.482403 0.058893 0.000000
4 0.068402 0.054134 2.553551 0.067426 0.000000
8 0.075794 0.054138 2.426632 0.073841 0.000000
16 0.104669 0.068705 2.044184 0.100762 0.000000
32 0.139227 0.069573 1.228228 0.131414 0.000000
64 0.188318 0.063255 0.907765 0.172693 0.000000
128 0.264706 0.052687 0.590516 0.233456 0.000000
256 0.416913 0.053419 0.453827 0.354413 0.000000
512 0.611965 0.060646 0.445669 0.486965 0.000000
1024 0.767452 0.057432 0.421641 0.517452 0.000000
2048 0.885113 0.037467 0.398855 0.385113 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.057551

Max cos²(θ): 0.070422

Min cos²(θ): 0.042068

Std cos²(θ): 0.011621

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.054994 0.054994
1 0.070422 0.070422
2 0.059095 0.059095
3 0.042068 0.042068
4 0.068530 0.068530
5 0.053046 0.053046
6 0.070022 0.070022
7 0.042234 0.042234

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

7. Individual Analysis - Run 6

Setup and Configuration

Summary Statistics (averaged across experts)

k align delta_vs_shuffle z_vs_shuffle effect_over_random cos_squared
1 0.096284 0.083204 2.714199 0.096039 0.096284
2 0.104348 0.087288 2.481372 0.103860 0.000000
4 0.118186 0.097865 2.627248 0.117210 0.000000
8 0.131431 0.098892 2.322079 0.129478 0.000000
16 0.141373 0.098440 2.420509 0.137467 0.000000
32 0.157609 0.093518 2.438773 0.149797 0.000000
64 0.186806 0.090480 2.143955 0.171181 0.000000
128 0.234749 0.082012 1.664156 0.203499 0.000000
256 0.328797 0.084129 1.319956 0.266297 0.000000
512 0.469418 0.083825 1.143750 0.344418 0.000000
1024 0.639959 0.070529 1.139612 0.389959 0.000000
2048 0.817105 0.041170 1.323049 0.317105 0.000000
4096 1.000000 0.000000 0.000000 0.000000 0.000000

Cos²(θ) Alignment (k=1)

Mean cos²(θ): 0.096284

Max cos²(θ): 0.112351

Min cos²(θ): 0.079784

Std cos²(θ): 0.012235

Per-expert cos²(θ) values:

Expertcos²(θ)align
0 0.088580 0.088580
1 0.108539 0.108539
2 0.084463 0.084463
3 0.079784 0.079784
4 0.101385 0.101385
5 0.089250 0.089250
6 0.112351 0.112351
7 0.105917 0.105917

Detailed Results by K Value

K = 1:

K = 2:

K = 4:

K = 8:

K = 16:

K = 32:

K = 64:

K = 128:

K = 256:

K = 512:

K = 1024:

K = 2048:

K = 4096:

Complete Analysis Plots

Comprehensive visualization of all metrics for this run.

Complete Analysis Visualization

See "Plot Explanations" section at the top of this report for detailed information about this plot.

Complete Analysis

Generated on 2025-12-27 16:56:22